Entanglement signatures of the small-world transition in Heisenberg-type models across network topologies

This paper investigates the Heisenberg model across diverse network topologies, and studying the variation of entanglement measures across these network topologies. Various network types are introduced along with their properties. An algorithm for generating networks using the Watts-Strogatz small world model is presented, focusing on the transition from regular to random networks via the small-world regime. The objective is to explore the entanglement landscape of the Heisenberg model across these network configurations, using extensive numerics. Insights into entanglement behaviour using graph theoretic properties such as local average clustering coefficient and the number of edge cuts during bipartitioning are provided. This opens up ways to analyze such complicated network topologies using entanglement.